Powerlaw Primer

I’m re-reading Clay Shirky’s excellent early work on powerlaws and am reminded that many people are still confused about what exactly a powerlaw is and under what circumstances it arises.

The first answer is easy: it’s basically any curve that has a y=1/x sort of shape, like the chart on the right. You can find powerlaws practically anywhere you look, from biology to book sales. The Long Tail is a powerlaw that isn’t cruelly cut off by bottlenecks in distribution such as limited shelf space and available channels.

The second answer is easy, too. Powerlaws come about when you have three conditions:

Variety

Inequality

Network effects (word of mouth, for example) to amplify the differences between them.

In others words, powerlaw distributions occur where things are different, some are better than others, and network effects can work to promote the good and suppress the bad. This results in what Vilfredo Pareto called the predictable imbalance of markets, culture and society: success breeds success, rich get richer and so on. Needless to say, these forces describe a good fraction of the world around us.